cp's OEIS Frontend

A224881 Expansion of 1/(1 - 16*x)^(1/8).

%I A224881 #25 Jun 23 2018 09:19:57
%S A224881 1,2,18,204,2550,33660,460020,6440280,91773990,1325624300,19354114780,
%T A224881 285033326760,4227994346940,63094684869720,946420273045800,
%U A224881 14259398780556720,215673406555920390,3273161111260438860,49824785804742235980,760483572809223601800
%N A224881 Expansion of 1/(1 - 16*x)^(1/8).
%H A224881 Seiichi Manyama, <a href="/A224881/b224881.txt">Table of n, a(n) for n = 0..500</a>
%F A224881 a(n) = (2^n/n!) * Product_{k=0..n-1} (8*k + 1).
%F A224881 a(n) ~ 16^n/(GAMMA(1/8)*n^(7/8)). - _Vaclav Kotesovec_, Jul 24 2013
%e A224881 G.f.: A(x) = 1 + 2*x + 18*x^2 + 204*x^3 + 2550*x^4 + 33660*x^5 + ...
%e A224881 where
%e A224881 A(x)^8 = 1 + 16*x + 256*x^2 + 4096*x^3 + 65536*x^4 + ... + 16^n*x^n + ...
%e A224881 Also,
%e A224881 A(x)^4 = 1 + 8*x + 96*x^2 + 1280*x^3 + 17920*x^4 + 258048*x^5 + ... + 4^n*A000984(n)*x^n + ...
%e A224881 A(x)^2 = 1 + 4*x + 40*x^2 + 480*x^3 + 6240*x^4 + 84864*x^5 + ... + 2^n*A004981(n)*x^n + ...
%p A224881 seq(coeff(series(1/(1-16*x)^(1/8), x,50),x,n+1),n=0..20); # _Muniru A Asiru_, Jun 23 2018
%t A224881 CoefficientList[Series[1/(1-16*x)^(1/8), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Jul 24 2013 *)
%o A224881 (PARI) {a(n)=polcoeff(1/(1-16*x +x*O(x^n))^(1/8),n)}
%o A224881 for(n=0,30,print1(a(n),", "))
%o A224881 (PARI) {a(n)=(2^n/n!)*prod(k=0,n-1,8*k + 1)}
%o A224881 for(n=0,30,print1(a(n),", "))
%o A224881 (GAP) List([0..20],n->(2^n/Factorial(n))*Product([0..n-1],k->8*k+1)); # _Muniru A Asiru_, Jun 23 2018
%Y A224881 (1-b*x)^(-1/A003557(b)): A000984 (b=4), A004981 (b=8), A004987 (b=9), A098658 (b=12), this sequence (b=16), A034688 (b=25), A298799 (b=27), A004993 (b=36), A034835 (b=49).
%Y A224881 Cf. A301271.
%K A224881 nonn
%O A224881 0,2
%A A224881 _Paul D. Hanna_, Jul 23 2013